Problem: Ishaan is $2$ times as old as Christopher. $35$ years ago, Ishaan was $7$ times as old as Christopher. How old is Ishaan now?
Explanation: We can use the given information to write down two equations that describe the ages of Ishaan and Christopher. Let Ishaan's current age be $i$ and Christopher's current age be $c$. The information in the first sentence can be expressed in the following equation: ${i = 2c}$ 35 years ago, Ishaan was $i - 35$ years old, and Christopher was $c - 35$ years old. The information in the second sentence can be expressed in the following equation: ${i - 35 = 7(c - 35)}$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $i$, it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$, we get: ${c = \dfrac{i}{2}}$. Substituting this into our second equation, we get: $ {i - 35 = 7 (}{\frac{i}{2}} {- 35)} $ which combines the information about $i$ from both of our original equations. Simplifying the right side of this equation, we get: $i - 35 = \dfrac{7}{2} i - 245$. Solving for $i$, we get: $\dfrac{5}{2} i = 210$. $i = \dfrac{2}{5} \cdot 210 = 84$.